(b) Suppose that

z=x^(2)-2xy^(2)

and that

x=rcos(\\\\theta ),y=rsin(\\\\theta )

.\ i. Sketch a tree diagram representing the dependencies of

z

on

x

and

y

, and

x

and\

y

on

r

and

\\\\theta

.\ ii. Find

(delz)/(delr)

using the tree diagram.\ iii. If

r=3

and

\\\\theta =(\\\\pi )/(6)

, find the value of

(delz)/(delr)

.

(b) Suppose that z=x22xy2 and that x=rcos(),y=rsin(). i. Sketch a tree diagram representing the dependencies of z on x and y, and x and y on r and . ii. Find rz using the tree diagram. iii. If r=3 and =6, find the value of rz